Find the number of words formed by permuting all the letters
of the word INDEPENDENCE such that the E's do not come together.

  1. 👍
  2. 👎
  3. 👁
  1. Use the "backdoor" approach,
    that is
    find the number of ways when they are together.

    then we have EEEE, I, N,N,N,D,D,P,C
    arrange 9 things, with 3N's and 2 D's
    = 9!/(3!2!)
    = 30240

    number of arrangements without restriction
    = 12!/(4!3!2!) = 1663200

    so number of ways when they are not together
    = 1663200 - 30240 = 1632960

    1. 👍
    2. 👎
  2. great answers

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. probobility

    4 -letter "words" are formed using the letters A, B, C, D, E, F, G. How many such words are possible for each of the following conditions? (a) No condition is imposed. Your answer is : Preview (b) No letter can be repeated in a

  2. Math Help

    In a certain state, each automobile license plate number consists of two letters followed by a four-digit number. To avoid confusion between "O" and zero and between "I" and one, the letters "O" and "I" are not used. How many

  3. math

    how many diferrent 9-letter words (real or imaginary) can be formed from the letters in the word ECONOMICS? the ans. must be 90,720

  4. Math

    A beverage company puts one of the letters in the word MATH under each bottle cap. A prize is given to each person who collects all the letters. Which of the following could be used as a simulation for how many bottles it would

  1. geometry

    In the English alphabet, there are 7 capital letters that look the same after being rotated 180∘. Those letters are H, I, N, O, S, X, and Z. How many different 3 letter "words" can be made from these letters such that when the

  2. math

    Find the number of words which can be formed by using the letters of the word EQUATION if each word has to start with a vowel. this a permutation question ans, choose are 40320 1260 1080 400 25200

  3. probability

    how many different 10-letter words (real or imaginary) can be formed from the letters in the word MONOCHROME?

  4. Check LA Answers

    What is etymology? (1 point) the pronunciation of a word the spelling of a word the history of a word the part of speech of a word*** What do etymological patterns help readers do?(1 point) define words pronounce words*** organize

  1. word unscramble

    need help unscrambling a word or words tarluna what is it HELP ME UNSCRAMBLE THESE LETTERS TO MAKE A WORD THAT PERTAINS TO SPACE AND IS A P POSSESSIVE NOUN. SEGHRTMLAN J'aodredefis Please post the word or words you need to

  2. Math 30-2

    How many distinguishable code symbols can be formed with the letters for the word PHILOSOPHICAL?

  3. math

    Find the number of the permutations with the letters of the word TRIANGLE.

  4. English

    what type of words are used to describe tone (1 point) A: Words that relate to a particual subject B: Words that evoke a particular feeling C: Words that have percise meanings D: Words that describe emotion (I have the answers for

You can view more similar questions or ask a new question.